Abstract
The theory of limit operators was developed by Rabinovich, Roch and Silbermann to study the Fredholmness of band-dominated operators on \(\ell ^p(\mathbb {Z}^N)\) for \(p \in \{0\} \cup [1,\infty ]\), and recently generalised to discrete metric spaces with Property A by Špakula and Willett for \(p \in (1,\infty )\). In this paper, we study the remaining extreme cases of \(p \in \{0,1,\infty \}\) (in the metric setting) to fill the gaps.
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Acknowledgements
First, I would like to thank Kang Li for suggesting this topic and some early discussions. I am also grateful to Ján Špakula, Baojie Jiang and Benyin Fu for several illuminating discussions and comments after reading some early drafts of this paper. I would like to express my sincere gratitude to Graham Niblo and Nick Wright for continuous support. Finally, I would like to thank the anonymous referee for several helpful suggestions.
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Supported by the Sino-British Trust Fellowship by Royal Society, International Exchanges 2017 Cost Share (China) grant EC\(\setminus \)NSFC\({\setminus }\)170341, and NSFC11871342.
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Zhang, J. Extreme Cases of Limit Operator Theory on Metric Spaces. Integr. Equ. Oper. Theory 90, 73 (2018). https://doi.org/10.1007/s00020-018-2498-7
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DOI: https://doi.org/10.1007/s00020-018-2498-7